Tayshaun Prince scored 10 for the Pistons, who scored the first nine points of the game but then lost the lead and struggled to take control against a banged-up team playing for the second straight night on the road.
Detroit pulled within one with a few minutes left. But Anthony converted a three-point play and Billups found his range from deep as Denver ended a 14-game losing streak in Auburn Hills.
Billups had lost his previous two games as a visitor at The Palace, where he's still adored by the fans and owner Karen Davidson, who shouted encouraging words at him in the final seconds.
"I love coming back here and feeling the love for all the blood and sweat I left in this building," Billups said. "It's fun because I'm home."
Billups, though, made it clear he's not happy with how Pistons coach John Kuester has benched Richard Hamilton without talking to him about the demotion.
"He's Pistons royalty," Billups said. "He's one of the greats, and his jersey is going up into those rafters, so he doesn't deserve to be disrespected like this."
Hamilton missed the game with the flu but likely wouldn't have played even if he was healthy because the Pistons have had some relative success -- winning five of seven -- since sitting him.
The Pistons might need Hamilton back on the court if Stuckey's injury is serious.
Stuckey left late in the first quarter with a bruised right shoulder after colliding with Anthony.
"I felt something pop," said Stuckey, adding he didn't think his shoulder was dislocated.
The Pistons were valued at $360 million -- a 25 percent decline since last year -- in Forbes' annual evaluation of NBA teams. Platinum Equity chairman Tom Gores, Detroit Tigers and Detroit Red Wings owner Mike Ilitch and The Postolos Group president George Postolos have expressed an interest in buying the team. ... Smith, who didn't play Tuesday against the Washington Wizards because he missed the shootaround, had eight points and made a spectacular dunk in the second half.